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      • Faculty Publications  (155)

      Mathematical ModelingRemove Mathematical Modeling →

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      • September 2025
      • Article

      Sticky Capital Controls

      By: Miguel Acosta-Henao, Laura Alfaro and Andrés Fernández
      There is much ongoing debate on the merits of capital controls as effective policy instruments. The differing perspectives are due in part to a lack of empirical studies that look at the intensive margin of controls, which in turn has prevented a quantitative... View Details
      Keywords: Capital Controls; Macroprudential Policies; Stickiness; Intensive; (S, S) Costs; Capital; Management; Macroeconomics; Governance Controls; Mathematical Methods
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      Acosta-Henao, Miguel, Laura Alfaro, and Andrés Fernández. "Sticky Capital Controls." Art. 104104. Journal of International Economics 157 (September 2025).
      • August 5, 2025
      • Article

      Data-driven Equation Discovery Reveals Nonlinear Reinforcement Learning in Humans

      By: Kyle J. LaFollette, Janni Yuval, Roey Schurr, David Melnikoff and Amit Goldenberg
      Computational models of reinforcement learning (RL) have significantly contributed to our understanding of human behavior and decision-making. Traditional RL models, however, often adopt a linear approach to updating reward expectations, potentially oversimplifying the... View Details
      Keywords: AI and Machine Learning; Behavior; Learning; Motivation and Incentives; Mathematical Methods
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      LaFollette, Kyle J., Janni Yuval, Roey Schurr, David Melnikoff, and Amit Goldenberg. "Data-driven Equation Discovery Reveals Nonlinear Reinforcement Learning in Humans." Proceedings of the National Academy of Sciences 122, no. 31 (August 5, 2025).
      • May–June 2025
      • Article

      Branch-and-Price for Prescriptive Contagion Analytics

      By: Alexandre Jacquillat, Michael Lingzhi Li, Martin Ramé and Kai Wang
      Contagion models are ubiquitous in epidemiology, social sciences, engineering, and management. This paper formulates a prescriptive contagion analytics model where a decision maker allocates shared resources across multiple segments of a population, each governed by... View Details
      Keywords: COVID-19; Mathematical Methods
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      Jacquillat, Alexandre, Michael Lingzhi Li, Martin Ramé, and Kai Wang. "Branch-and-Price for Prescriptive Contagion Analytics." Operations Research 73, no. 3 (May–June 2025): 1558–1580.
      • May–June 2025
      • Article

      Slowly Varying Regression Under Sparsity

      By: Dimitris Bertsimas, Vassilis Digalakis Jr, Michael Lingzhi Li and Omar Skali Lami
      We consider the problem of parameter estimation in slowly varying regression models with sparsity constraints. We formulate the problem as a mixed integer optimization problem and demonstrate that it can be reformulated exactly as a binary convex optimization problem... View Details
      Keywords: Mathematical Methods; Analytics and Data Science
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      Bertsimas, Dimitris, Vassilis Digalakis Jr, Michael Lingzhi Li, and Omar Skali Lami. "Slowly Varying Regression Under Sparsity." Operations Research 73, no. 3 (May–June 2025): 1581–1597.
      • 2025
      • Working Paper

      Incentive-Compatible Recovery from Manipulated Signals, with Applications to Decentralized Physical Infrastructure

      By: Jason Milionis, Jens Ernstberger, Joseph Bonneau, Scott Duke Kominers and Tim Roughgarden
      We introduce the first formal model capturing the elicitation of unverifiable information from a party (the "source") with implicit signals derived by other players (the "observers"). Our model is motivated in part by applications in decentralized physical... View Details
      Keywords: Mathematical Methods; Infrastructure; Information Infrastructure
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      Milionis, Jason, Jens Ernstberger, Joseph Bonneau, Scott Duke Kominers, and Tim Roughgarden. "Incentive-Compatible Recovery from Manipulated Signals, with Applications to Decentralized Physical Infrastructure." Working Paper, March 2025.
      • November 2024
      • Article

      Preference Externality Estimators: A Comparison of Border Approaches and IVs

      By: Xi Ling, Wesley R. Hartmann and Tomomichi Amano
      This paper compares two estimators—the Border Approach and an Instrumental Variable (IV) estimator—using a unified framework where identifying variation arises from “preference externalities,” following the intuition in Waldfogel (2003). We highlight two dimensions in... View Details
      Keywords: Econometrics; Casual Inference; Marketing; Economics; Advertising; Mathematical Methods
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      Ling, Xi, Wesley R. Hartmann, and Tomomichi Amano. "Preference Externality Estimators: A Comparison of Border Approaches and IVs." Management Science 70, no. 11 (November 2024): 7892–7910.
      • 2024
      • Working Paper

      Pitfalls of Demographic Forecasts of U.S. Elections

      By: Richard Calvo, Vincent Pons and Jesse M. Shapiro
      Many observers have forecast large partisan shifts in the US electorate based on demographic trends. Such forecasts are appealing because demographic trends are often predictable even over long horizons. We backtest demographic forecasts using data on US elections... View Details
      Keywords: Mathematical Methods; Voting; Political Elections; Trends; Forecasting and Prediction; Demographics
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      Calvo, Richard, Vincent Pons, and Jesse M. Shapiro. "Pitfalls of Demographic Forecasts of U.S. Elections." NBER Working Paper Series, No. 33016, October 2024.
      • 2024
      • Article

      A Universal In-Place Reconfiguration Algorithm for Sliding Cube-Shaped Robots in Quadratic Time

      By: Zachary Abel, Hugo A. Akitaya, Scott Duke Kominers, Matias Korman and Frederick Stock
      In the modular robot reconfiguration problem we are given n cube-shaped modules (or "robots") as well as two configurations, i.e., placements of the n modules so that their union is face-connected. The goal is to find a sequence of moves that reconfigures the modules... View Details
      Keywords: Robots; Mathematical Methods
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      Abel, Zachary, Hugo A. Akitaya, Scott Duke Kominers, Matias Korman, and Frederick Stock. "A Universal In-Place Reconfiguration Algorithm for Sliding Cube-Shaped Robots in Quadratic Time." Proceedings of the International Symposium on Computational Geometry (SoCG) 40th (2024): 1:1–1:14.
      • June 2024
      • Article

      Redistributive Allocation Mechanisms

      By: Mohammad Akbarpour, Piotr Dworczak and Scott Duke Kominers
      Many scarce public resources are allocated at below-market-clearing prices, and sometimes for free. Such "non-market" mechanisms sacrifice some surplus, yet they can potentially improve equity. We develop a model of mechanism design with redistributive concerns. Agents... View Details
      Keywords: Equality and Inequality; Welfare; Mathematical Methods; Market Design; Cost vs Benefits
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      Akbarpour, Mohammad, Piotr Dworczak, and Scott Duke Kominers. "Redistributive Allocation Mechanisms." Journal of Political Economy 132, no. 6 (June 2024): 1831–1875. (Authors' names are in certified random order.)
      • 2024
      • Working Paper

      Anytime-Valid Inference in Linear Models and Regression-Adjusted Causal Inference

      By: Michael Lindon, Dae Woong Ham, Martin Tingley and Iavor I. Bojinov
      Linear regression adjustment is commonly used to analyze randomized controlled experiments due to its efficiency and robustness against model misspecification. Current testing and interval estimation procedures leverage the asymptotic distribution of such estimators to... View Details
      Keywords: Mathematical Methods; Analytics and Data Science
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      Lindon, Michael, Dae Woong Ham, Martin Tingley, and Iavor I. Bojinov. "Anytime-Valid Inference in Linear Models and Regression-Adjusted Causal Inference." Harvard Business School Working Paper, No. 24-060, March 2024.
      • 2023
      • Article

      Balancing Risk and Reward: An Automated Phased Release Strategy

      By: Yufan Li, Jialiang Mao and Iavor Bojinov
      Phased releases are a common strategy in the technology industry for gradually releasing new products or updates through a sequence of A/B tests in which the number of treated units gradually grows until full deployment or deprecation. Performing phased releases in a... View Details
      Keywords: Product Launch; Mathematical Methods; Product Development
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      Li, Yufan, Jialiang Mao, and Iavor Bojinov. "Balancing Risk and Reward: An Automated Phased Release Strategy." Advances in Neural Information Processing Systems (NeurIPS) (2023).
      • 2023
      • Article

      Verifiable Feature Attributions: A Bridge between Post Hoc Explainability and Inherent Interpretability

      By: Usha Bhalla, Suraj Srinivas and Himabindu Lakkaraju
      With the increased deployment of machine learning models in various real-world applications, researchers and practitioners alike have emphasized the need for explanations of model behaviour. To this end, two broad strategies have been outlined in prior literature to... View Details
      Keywords: AI and Machine Learning; Mathematical Methods
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      Bhalla, Usha, Suraj Srinivas, and Himabindu Lakkaraju. "Verifiable Feature Attributions: A Bridge between Post Hoc Explainability and Inherent Interpretability." Advances in Neural Information Processing Systems (NeurIPS) (2023).
      • 2023
      • Article

      Which Models Have Perceptually-Aligned Gradients? An Explanation via Off-Manifold Robustness

      By: Suraj Srinivas, Sebastian Bordt and Himabindu Lakkaraju
      One of the remarkable properties of robust computer vision models is that their input-gradients are often aligned with human perception, referred to in the literature as perceptually-aligned gradients (PAGs). Despite only being trained for classification, PAGs cause... View Details
      Keywords: AI and Machine Learning; Mathematical Methods
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      Srinivas, Suraj, Sebastian Bordt, and Himabindu Lakkaraju. "Which Models Have Perceptually-Aligned Gradients? An Explanation via Off-Manifold Robustness." Advances in Neural Information Processing Systems (NeurIPS) (2023).
      • 2023
      • Working Paper

      Causal Interpretation of Structural IV Estimands

      By: Isaiah Andrews, Nano Barahona, Matthew Gentzkow, Ashesh Rambachan and Jesse M. Shapiro
      We study the causal interpretation of instrumental variables (IV) estimands of nonlinear, multivariate structural models with respect to rich forms of model misspecification. We focus on guaranteeing that the researcher's estimator is sharp zero consistent, meaning... View Details
      Keywords: Mathematical Methods
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      Andrews, Isaiah, Nano Barahona, Matthew Gentzkow, Ashesh Rambachan, and Jesse M. Shapiro. "Causal Interpretation of Structural IV Estimands." NBER Working Paper Series, No. 31799, October 2023.
      • 2023
      • Article

      On Minimizing the Impact of Dataset Shifts on Actionable Explanations

      By: Anna P. Meyer, Dan Ley, Suraj Srinivas and Himabindu Lakkaraju
      The Right to Explanation is an important regulatory principle that allows individuals to request actionable explanations for algorithmic decisions. However, several technical challenges arise when providing such actionable explanations in practice. For instance, models... View Details
      Keywords: Mathematical Methods; Analytics and Data Science
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      Meyer, Anna P., Dan Ley, Suraj Srinivas, and Himabindu Lakkaraju. "On Minimizing the Impact of Dataset Shifts on Actionable Explanations." Proceedings of the Conference on Uncertainty in Artificial Intelligence (UAI) 39th (2023): 1434–1444.
      • 2023
      • Working Paper

      How People Use Statistics

      By: Pedro Bordalo, John J. Conlon, Nicola Gennaioli, Spencer Yongwook Kwon and Andrei Shleifer
      We document two new facts about the distributions of answers in famous statistical problems: they are i) multi-modal and ii) unstable with respect to irrelevant changes in the problem. We offer a model in which, when solving a problem, people represent each hypothesis... View Details
      Keywords: Decision Choices and Conditions; Microeconomics; Mathematical Methods; Behavioral Finance
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      Bordalo, Pedro, John J. Conlon, Nicola Gennaioli, Spencer Yongwook Kwon, and Andrei Shleifer. "How People Use Statistics." NBER Working Paper Series, No. 31631, August 2023.
      • July 2023 (Revised July 2023)
      • Background Note

      Generative AI Value Chain

      By: Andy Wu and Matt Higgins
      Generative AI refers to a type of artificial intelligence (AI) that can create new content (e.g., text, image, or audio) in response to a prompt from a user. ChatGPT, Bard, and Claude are examples of text generating AIs, and DALL-E, Midjourney, and Stable Diffusion are... View Details
      Keywords: AI; Artificial Intelligence; Model; Hardware; Data Centers; AI and Machine Learning; Applications and Software; Analytics and Data Science; Value
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      Wu, Andy, and Matt Higgins. "Generative AI Value Chain." Harvard Business School Background Note 724-355, July 2023. (Revised July 2023.)
      • 2023
      • Article

      Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse

      By: Martin Pawelczyk, Teresa Datta, Johannes van-den-Heuvel, Gjergji Kasneci and Himabindu Lakkaraju
      As machine learning models are increasingly being employed to make consequential decisions in real-world settings, it becomes critical to ensure that individuals who are adversely impacted (e.g., loan denied) by the predictions of these models are provided with a means... View Details
      Keywords: AI and Machine Learning; Decision Choices and Conditions; Mathematical Methods
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      Pawelczyk, Martin, Teresa Datta, Johannes van-den-Heuvel, Gjergji Kasneci, and Himabindu Lakkaraju. "Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse." Proceedings of the International Conference on Learning Representations (ICLR) (2023).
      • 2023
      • Working Paper

      Distributionally Robust Causal Inference with Observational Data

      By: Dimitris Bertsimas, Kosuke Imai and Michael Lingzhi Li
      We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds in two steps. We first... View Details
      Keywords: AI and Machine Learning; Mathematical Methods
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      Bertsimas, Dimitris, Kosuke Imai, and Michael Lingzhi Li. "Distributionally Robust Causal Inference with Observational Data." Working Paper, February 2023.
      • 2022
      • Article

      Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations

      By: Tessa Han, Suraj Srinivas and Himabindu Lakkaraju
      A critical problem in the field of post hoc explainability is the lack of a common foundational goal among methods. For example, some methods are motivated by function approximation, some by game theoretic notions, and some by obtaining clean visualizations. This... View Details
      Keywords: Mathematical Methods; Decision Choices and Conditions; Analytics and Data Science
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      Han, Tessa, Suraj Srinivas, and Himabindu Lakkaraju. "Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations." Advances in Neural Information Processing Systems (NeurIPS) (2022). (Best Paper Award, International Conference on Machine Learning (ICML) Workshop on Interpretable ML in Healthcare.)
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